Ensemble Finite Element Solvers for Cardiovascular Modeling under Uncertainty

Computational models are increasingly used for diagnosis and treatment of cardiovascular disease. To provide a quantitative hemodynamic understanding that can be effectively used in the clinic, it is crucial to quantify the variability in the outputs from these models due to multiple sources of uncertainty. To quantify this variability, the analyst invariably needs to generate a large collection of high-fidelity model solutions, typically requiring a substantial computational effort. In this dissertation, we show how an explicit-in-time ensemble cardiovascular solver offers superior performance with respect to the embarrassingly parallel solution with implicit-in-time algorithms, typical of an inner-outer loop paradigm for non-intrusive uncertainty propagation. We discuss in detail the numerics and efficient distributed implementation of a segregated FSI cardiovascular solver on both CPU and GPU systems, and demonstrate its applicability to idealized and patient-specific cardiovascular models, analyzed under steady and pulsatile flow conditions.